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# If 2^x-2^(x-2)=3*2^13 what is the value of x?

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Intern
Joined: 15 Sep 2011
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If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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15 Oct 2011, 12:26
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If $$2^x-2^{(x-2)}=3*2^{13}$$ what is the value of x?

A. 9
B. 11
C. 13
D. 15
E. 17

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.html
[Reveal] Spoiler: OA

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Manager
Joined: 21 Aug 2010
Posts: 186

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Location: United States
GMAT 1: 700 Q49 V35
Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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15 Oct 2011, 13:43
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele

If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17

Q:2^x- 2^(x-2) = 3(2^13)

==>2^x = 3(2^13)+2^(x-2)

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )
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Kudos [?]: 133 [0], given: 141

Manager
Joined: 21 Aug 2010
Posts: 186

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GMAT 1: 700 Q49 V35
Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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15 Oct 2011, 13:52
3
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gopu106 wrote:
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele

If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17

Q:2^x- 2^(x-2) = 3(2^13)

==>2^x = 3(2^13)+2^(x-2)

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )

Another way

Q:2^x- 2^(x-2) = 3(2^13)

==>[2^2 * 2^(x-2)] - 2^(x-2) = 3(2^13)
==>4[2^(x-2)] - 2^(x-2) = 3(2^13)
==>3[2^(x-2)] = 3(2^13)

==>x-2 = 13
x=15 (D)
_________________

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Kudos [?]: 133 [3], given: 141

Manager
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Posts: 171

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WE: Information Technology (Investment Banking)
Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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15 Oct 2011, 23:35
3
KUDOS
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15

Kudos [?]: 102 [3], given: 1

Intern
Joined: 15 Sep 2011
Posts: 2

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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16 Oct 2011, 01:13
Thanks a lot to both of you!!! now it is really clear

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Intern
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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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27 Mar 2016, 17:46
subhajeet wrote:
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15

How do you take 2^(x-2) as a/4?Can you explain please

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Math Expert
Joined: 02 Sep 2009
Posts: 42247

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Re: If 2^x-2^(x-2)=3*2^13 what is the value of x? [#permalink]

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28 Mar 2016, 02:06
2
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Expert's post
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theperfectgentleman wrote:
subhajeet wrote:
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15

How do you take 2^(x-2) as a/4?Can you explain please

$$2^{x-2} = 2^x*2^{-2}=\frac{2^x}{4}=\frac{a}{4}$$

If $$2^x-2^{x-2}=3*2^{13}$$ what is the value of x?
A. 9
B. 11
C. 13
D. 15
E. 17

$$2^x-2^{x-2}=3*2^{13}$$ --> $$2^x-2^{x}*2^{-2}=3*2^{13}$$ --> $$2^x-\frac{2^{x}}{2^{2}}=3*2^{13}$$ --> $$2^x(1-\frac{1}{2^{2}})=3*2^{13}$$ --> $$2^x*\frac{3}{2^{2}}=3*2^{13}$$ --> $$2^x=2^{15}$$ --> $$x=15$$.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.html
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Kudos [?]: 132674 [2], given: 12331

Re: If 2^x-2^(x-2)=3*2^13 what is the value of x?   [#permalink] 28 Mar 2016, 02:06
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